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The auxiliary function method consists of taking full advantage of the expansion of the phase function on spherical harmonics in order to deduce an integral equation from the radiative transfer equation. In contrast to the discrete-ordinate method, it is free of the channel concept, the unknowns being a function only of the optical depth. After presenting the method, we show that it is very accurate and particularly well fitted when the scattering medium is continuously inhomogeneous in albedo and phase function and also for sublayers with different refractive index.

To model bidirectional measurements, a numerical method for computing the incoherent light scattered by a diffusing medium is presented. The results are expressed as a function of the incident and the observer angles (theta(i), phi(i)) and (theta(f), phi(f)), in contrast to the N-flux method, which gives no information about the azimuthal-distribution. To solve the multiple-scattering equations, an auxiliary function, expanded on the spherical harmonics, is introduced in the diffusion equation. A set of integral equations on the coefficients are obtained that are well suited for the numerical resolution. The boundary conditions are included in the linear operator of the integral equation, so that each boundary condition is associated with a specific equation. As an illustration, the method is applied to numerical simulations of maps of the light scattered by a thick refractive diffusing layer of refractive index n = 1.5, for two directive phase functions and for several incident collimated-beam angles.

The objective of this paper is to extend the amount of exact solutions for acoustic scattering configurations available to validate numerical methods. The configuration chosen is the radiation of an acoustic point source located at the center of a rigid spherical shell having a circular aperture. In comparison to standard scattering problems, like diffraction of a plane wave by a closed sphere, this problem implies a more severe geometry including a sharp edge. The exact solution is derived using an expansion of the pressure field in terms of spherical Bessel functions and Legendre polynomials. The associated coefficients are the solution to an infinite linear system. The truncation of this system as a function of the reduced wave number ka is discussed. It is found that the system is stable with regard to the truncation and that only 4×ka coefficients are needed to get an accurate solution. Comparisons are made with solutions obtained using a boundary integral method developed by Hamdi [‘‘Formulation var...

Wave extrapolation methods are commonly used to evaluate the farfield radiation pattern of a complex source from nearfield measurements. The nearfield data are usually collected with transducer arrays or matrices. This standard procedure poses problems of signal conditioning, calibration, and recording that may be avoided by performing a synthetic detection of the nearfield. This alternate procedure, which borrows its principle from the field of synthetic aperture radar (SAR), is explored and illustrated in this article. The problem of radial wave extrapolation in a layered configuration is also analyzed. Acoustic wave radiation from a uniform stream to a region at rest is specifically considered. Exact and approximate wave extrapolators are derived. Comparisons between experimental measurements and wave extrapolation results indicate that the combination of synthetic nearfield detection and radial wave extrapolation is reliable and that extrapolation in layered situations may be carried out with little a...

The existence of a large scale structure of turbulence in a free hot jet is emphasized by measurements carried out on the initial assumption of a fine scale structure. Second order analysis allows one to split the signals picked up in the jet and in the acoustic field into coherent and non-coherent components. The validity of this decomposition with regard to the physical picture of the phenomenon, i.e. vortices convected in the mixing zone, is tested by means of conditional sampling analysis, applied for several diagnostics.

We present a family with four children born to second-cousin parents. Two of the children had myoclonic epilepsy, congenital deafness, a dystrophic pattern of the macular pigment epithelium, incomplete right bundle branch block, and psychiatric disorders appearing after fever episodes. Results of all laboratory investigations including mitochondrial DNA analysis were normal. Despite the fact that this condition resembles one reported by Latham and Munro in 1937, it is possible that we might be reporting on a new autosomal recessive syndrome.

A major task within the European Community funded Project SILENCE(R), was to flight-test high-lift devices low-noise modifications and landing gear noise reduction fairings. This work was part of the airframe noise reduction investigation that was initiated in 2001, with a design based on both computational and experimental work, aiming at modifications that fit the actual Airbus A340-300 test aircraft. Landing-gear fairings were designed and manufactured by both Airbus and Messier-Dowty. They are add-on elements that can be mounted on the existing gears without affecting the operation of the landing gear. The add-on treatment modifications (designed and manufactured by Airbus) on the high-lift devices consist of covering the numerous cavities in the slat-retraction system and flap-side edge space, that have been identified to be responsible for a significant part of the noise. The tests were conducted in September 2003 at Tarbes airport. To investigate the noise perceived on the ground, Airbus’ noise system of microphones was used. To help the result interpretation and detection of possible spurious effects, a large array of microphones was operated by ONERA and DLR. On board measurements (pressure and acceleration sensors, strain gages, etc.) were also implemented to assess local effect of devices. Back-to-back tests were achieved in 11 flights, by successively removing all modifications in small groups. Examples of the effect of SILENCE(R) devices is assessed for typical landing configuration and also for specific aerodynamic noise configurations, that were designed to separate the effects of landing gear and high-lift device noise reduction.

W the analog representation for jet noise studies allows the prediction of the dimensional laws for acoustic emission, a better understanding of the'acoustic far field requires a more physical picture of the acousticgenerating mechanisms. In particular, in a previous work a direct experimental estimation of the acoustic intensity associated with the large-scale structure of turbulence was obtained, on the basis of the same assumptions allowing the full use of the second-order analysis on signals recorded inside and outside the jet. Here, a more general method, based on conditional sampling, is proposed for jet noise source localization. It consists of selecting, through a detection criterion > imposed on a selected signal, a set of samples representative of the passage of wave packets, and working on an ensemble of these sets rather than on time averages. In this manner, each generating mechanism can be selected by a proper choice of the detection criterion, and its acoustic efficiency computed. In addition, ensemble averages avoid the limitations due to time averages, and lead to a better signal/noise ratio when the classical correlation function is very weak.